{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BW56D2JBYX6C46JFI6FN3EIH2E","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f1390e28e42fa00b3def35fe5099bc9b55866d35383318f873a1a9c2710a582a","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-05T09:30:48Z","title_canon_sha256":"b21abaecff94acd33db43e3548d56dda0c132f1c1ad98a227b6de4bc1e523921"},"schema_version":"1.0","source":{"id":"1109.0838","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0838","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0838v2","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0838","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"BW56D2JBYX6C","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BW56D2JBYX6C46JF","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BW56D2JB","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:9423935eb12b72acd1a8d91a009b12ad17e5850b15e41c06923fe8c0a75a35f0","target":"graph","created_at":"2026-05-18T03:51:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k = g(\\varepsilon_{k-s}, s \\in \\Z^d)$, $k\\in\\Z^d$, where $(\\varepsilon_i)_{i\\in\\Z^d}$ are i.i.d random variables and $g$ is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying d","authors_text":"Dalibor Volny (LMRS), Mohamed El Machkouri (LMRS), Wei Biao Wu","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-05T09:30:48Z","title":"A central limit theorem for stationary random fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0838","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ca543502ba172dd3146802768b2ac851e9f1a3a53215ba44fb87355da157b7ac","target":"record","created_at":"2026-05-18T03:51:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f1390e28e42fa00b3def35fe5099bc9b55866d35383318f873a1a9c2710a582a","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-05T09:30:48Z","title_canon_sha256":"b21abaecff94acd33db43e3548d56dda0c132f1c1ad98a227b6de4bc1e523921"},"schema_version":"1.0","source":{"id":"1109.0838","kind":"arxiv","version":2}},"canonical_sha256":"0dbbe1e921c5fc2e7925478add9107d13e05434e114d91ddd617165ce52cc263","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dbbe1e921c5fc2e7925478add9107d13e05434e114d91ddd617165ce52cc263","first_computed_at":"2026-05-18T03:51:14.386219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:14.386219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qJnb7qlltvnhqE26Sav8LCLIKxgDwWH7Kf6gn0d8QVVCGC8PEygTSP5B49+ypULpDKwi9/SbncE0atN75JDZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:14.386663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0838","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca543502ba172dd3146802768b2ac851e9f1a3a53215ba44fb87355da157b7ac","sha256:9423935eb12b72acd1a8d91a009b12ad17e5850b15e41c06923fe8c0a75a35f0"],"state_sha256":"3aa08d7b7dab1e4673e4786f1423c88210141ffc54433e8fec2a97f19df6fe5a"}